# Chi-Square Curve

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## Definition: Chi-Square Curve

The distribution of the chi-square statistic is called the chi-square distribution. In a statistical experiment of a random sample of size n, having a standard deviation equal to σ, the standard deviation of the sample is equal to s. A statistic, called chi-square, is defined using the following equation:

Χ^2 = [ ( n - 1 ) * s^2 ] / σ^2

If this experiment is repeated an infinite number of times, a sampling distribution for the chi-square statistic is obtained.

The chi-square distribution has the following properties:

• The mean of the distribution is equal to the number of degrees of freedom: μ = v.
• The variance is equal to two times the number of degrees of freedom: σ^2 = 2 * v
• When the degrees of freedom are greater than or equal to 2, the maximum value for Y occurs when Χ^2 = v - 2.
• As the degrees of freedom increase, the chi-square curve approaches a normal distribution.

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